CN113873429B - Underground tunnel-oriented ridge regression two-dimensional positioning method and system - Google Patents

Underground tunnel-oriented ridge regression two-dimensional positioning method and system Download PDF

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Publication number
CN113873429B
CN113873429B CN202111166363.9A CN202111166363A CN113873429B CN 113873429 B CN113873429 B CN 113873429B CN 202111166363 A CN202111166363 A CN 202111166363A CN 113873429 B CN113873429 B CN 113873429B
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positioning
base station
representing
ridge regression
signal
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CN113873429A (en
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梁伟
尹康涌
黄浩声
陶风波
张恒
林元棣
朱睿
王静君
贾萌萌
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State Grid Jiangsu Electric Power Co Ltd
Electric Power Research Institute of State Grid Jiangsu Electric Power Co Ltd
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State Grid Jiangsu Electric Power Co Ltd
Electric Power Research Institute of State Grid Jiangsu Electric Power Co Ltd
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/02—Services making use of location information
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/30—Services specially adapted for particular environments, situations or purposes
    • H04W4/33—Services specially adapted for particular environments, situations or purposes for indoor environments, e.g. buildings
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W64/00—Locating users or terminals or network equipment for network management purposes, e.g. mobility management

Abstract

The application relates to the technical field of tunnel positioning and discloses a ridge regression two-dimensional positioning method and system for an underground tunnel. In the method, the TDOA value is obtained by receiving the signal arrival time from different positioning base stations through the positioning tag. And further determining an observation vector and a design matrix of the least square problem according to the position of the base station. The condition number after the transpose of the design matrix and the multiplication of the design matrix are calculated to estimate the noise sensitivity, and a proper ridge regression coefficient is set based on the condition number. And finally, determining a position vector, and determining the coordinates of the positioning tag according to the position vector. Through the steps, the method overcomes the noise sensitivity commonly existing in TDOA positioning in the underground tunnel environment, and greatly improves the positioning precision and stability.

Description

Underground tunnel-oriented ridge regression two-dimensional positioning method and system
Technical Field
The application relates to the technical field of tunnel positioning, in particular to a ridge regression two-dimensional positioning method and system for an underground tunnel.
Background
With the advancement of urban design, the living and production environments in urban circles are gradually transferred from the ground to the underground. The environments such as underground business circles, underground power grid tunnels and the like cannot be positioned by utilizing satellites because satellite signals are blocked, wherein the position information of personnel has important significance for business application and personnel security.
At present, a least square positioning method is generally adopted for positioning in an underground tunnel, and specifically, a method based on weighted least square such as least square and Chan algorithm is adopted. However, compared with widely used indoor positioning technology, the underground tunnel focuses on a pipe gallery environment with a large length-width ratio, the environment is constrained by geographic factors, and when a least square positioning method is used, the sensitivity to noise is high due to the inverse of a disease state matrix in a solution method, and a large positioning error can be caused by a small ranging error.
Disclosure of Invention
The application discloses a ridge regression two-dimensional positioning method and system for an underground tunnel, which are used for solving the technical problems that in the prior art, compared with widely used indoor positioning technology, the underground tunnel is focused on a pipe gallery environment with a large length-width ratio, the environment is constrained by geographic factors, and when a traditional least square positioning method is used, due to the fact that a disease state matrix is inverted in a solution, sensitivity to noise is very high, and a very large positioning error is caused by a small distance measurement error.
The first aspect of the application discloses a ridge regression two-dimensional positioning method facing an underground tunnel, the method is applied to positioning labels in the underground tunnel, a plurality of positioning base stations are arranged on two sides of a channel of the underground tunnel, and the ridge regression two-dimensional positioning method facing the underground tunnel comprises the following steps:
the positioning tag acquires signals of any positioning base station and acquires signal arrival time of the any positioning base station;
the positioning tag determines the base station position of any positioning base station according to the signals of any positioning base station;
the positioning tag determines a reference signal according to the signal arrival time of any positioning base station, wherein the reference signal is a signal of the positioning base station which is firstly acquired by the positioning tag;
the positioning tag determines a TDOA value according to the signal of any positioning base station and the reference signal, wherein the TDOA value refers to the difference value between the arrival time of other signals and the arrival time of the reference signal; the other signal arrival time refers to signal arrival time of other signals except the reference signal in the signals of the positioning base station; the reference signal arrival time refers to a signal arrival time of the reference signal;
the positioning tag obtains the propagation speed of signals and determines an observation vector and a design matrix according to the base station position of any positioning base station, the TDOA value and the propagation speed of the signals;
the positioning label determines a ridge regression coefficient according to the design matrix and a preset condition number limit;
the positioning label determines a position vector according to the observation vector, the design matrix and the ridge regression coefficient;
and the positioning label determines the coordinates of the positioning label according to the position vector.
Optionally, the condition number is limited to a condition number less than 1000.
Optionally, the positioning tag determines a ridge regression coefficient according to the design matrix and a preset condition number limit, including:
the ridge regression coefficients are determined by the following formula:
min λ＞0 λ；
s.t.cond(G T G+λI)＜1000；
wherein λ represents the ridge regression coefficient, cond (·) represents the condition number of the matrix, G represents the design matrix, T represents the transpose of the matrix, I represents the identity matrix, the number of rows and columns of the identity matrix I and G T The number of rows and columns of G is the same.
Optionally, the positioning tag determines a position vector according to the observation vector, the design matrix and the ridge regression coefficient, including:
the position vector is determined by the following formula:
θ＝(G T G+λI) -1 G T h；
wherein θ represents the position vector, G represents the design matrix, T represents the transpose of the matrix, λ represents the ridge regression coefficient, h represents the observation vector, I represents the identity matrix, and the number of rows and columns of the identity matrix I and G T The number of rows and columns of G is the same.
Optionally, the determining, by the positioning tag, coordinates of the positioning tag according to the position vector includes:
the coordinates of the positioning tag are determined by the following formula:
u＝θ(1∶2)；
where u represents the coordinates of the positioning tag and θ (1:2) represents the first two elements of the position vector θ.
Optionally, the positioning tag obtains a propagation speed of a signal, and determines an observation vector and a design matrix according to a base station position of any positioning base station, the TDOA value, and the propagation speed of the signal, including:
the observation vector is determined by the following formula:
wherein h (j) represents a j-th element of the observation vector, c represents a preset signal propagation speed, Δt (j) represents a j-th element in the TDOA value,representing the square of the vector's two norms, s j+1 The j+1th element, s, representing the base station position 1 And representing the base station position of a reference base station, wherein the reference base station refers to the position of the positioning base station acquired by the positioning tag first.
Optionally, the positioning tag obtains a propagation speed of a signal, and determines an observation vector and a design matrix according to a base station position of any positioning base station, the TDOA value, and the propagation speed of the signal, including:
the design matrix is determined by the following formula:
G(i，：)＝[-2(s i+1 -s 1 ) T c·Δt(i)]；
wherein G (i: represents the ith row, s of the design matrix i+1 The (i+1) th element, s, representing the position of the base station 1 And representing the base station position of a reference base station, wherein the reference base station refers to the position of the positioning base station which is firstly acquired by the positioning tag, T represents the transposition of a matrix, c represents the preset signal propagation speed, and delta T (i) represents the ith element in the TDOA value.
Optionally, the positioning base station includes: UWB positioning base station, bluetooth positioning base station and ultrasonic positioning base station.
The second aspect of the application discloses a ridge regression two-dimensional positioning system facing an underground tunnel, the ridge regression two-dimensional positioning system facing the underground tunnel applies the ridge regression two-dimensional positioning method facing the underground tunnel disclosed in the first aspect of the application, the system is applied to positioning labels in the underground tunnel, a plurality of positioning base stations are arranged on two sides of a channel of the underground tunnel, and the ridge regression two-dimensional positioning system facing the underground tunnel comprises:
the signal receiving module is used for acquiring signals of any positioning base station by the positioning tag and acquiring signal arrival time of any positioning base station;
the base station position acquisition module is used for determining the base station position of any positioning base station according to the signals of any positioning base station by the positioning tag;
the reference signal acquisition module is used for determining a reference signal according to the signal arrival time of any positioning base station by the positioning tag, wherein the reference signal is a signal of the positioning base station which is acquired by the positioning tag first;
the TDOA value determining module is used for determining a TDOA value according to the signal of any positioning base station and the reference signal, wherein the TDOA value refers to the difference value between the arrival time of other signals and the arrival time of the reference signal; the other signal arrival time refers to signal arrival time of other signals except the reference signal in the signals of the positioning base station; the reference signal arrival time refers to a signal arrival time of the reference signal;
the vector and matrix processing module is used for acquiring the propagation speed of the signals by the positioning tag and determining an observation vector and a design matrix according to the base station position of any positioning base station, the TDOA value and the propagation speed of the signals;
the ridge regression coefficient determining module is used for determining a ridge regression coefficient according to the design matrix and the preset condition number limit by the positioning label;
the position vector determining module is used for determining a position vector according to the observation vector, the design matrix and the ridge regression coefficient by the positioning label;
and the positioning module is used for determining the coordinates of the positioning label according to the position vector by the positioning label.
Optionally, the ridge regression coefficient determination module is configured to determine the ridge regression coefficient by the following formula:
min λ＞0 λ；
s.t.cond(G T G+λI)＜1000；
wherein λ represents the ridge regression coefficient, cond (·) represents the condition number of the matrix, G represents the design matrix, T represents the transpose of the matrix, I represents the identity matrix, the number of rows and columns of the identity matrix I and G T The number of rows and columns of G is the same.
Optionally, the location vector determining module is configured to determine the location vector by the following formula:
θ＝(G T G+λI) -1 G T h；
wherein θ represents the position vector, G represents the design matrix, T represents the transpose of the matrix, λ represents the ridge regression coefficient, h represents the observation vector, I represents the identity matrix, and the number of rows and columns of the identity matrix I and G T The number of rows and columns of G is the same.
Optionally, the positioning module is configured to determine coordinates of the positioning tag by the following formula:
u＝θ(1∶2)；
where u represents the coordinates of the positioning tag and θ (1:2) represents the first two elements of the position vector θ.
Optionally, the vector and matrix processing module is configured to determine the observation vector by the following formula:
wherein h (j) represents a j-th element of the observation vector, c represents a preset signal propagation speed, Δt (j) represents a j-th element in the TDOA value,representing the square of the vector's two norms, s j+1 The j+1th element, s, representing the base station position 1 And representing the base station position of a reference base station, wherein the reference base station refers to the position of the positioning base station acquired by the positioning tag first.
Optionally, the vector and matrix processing module is configured to determine the design matrix by the following formula:
G(i，：)＝[-2(s i+1 -s 1 ) T c·Δt(i)]；
wherein G (i: represents the ith row, s of the design matrix i+1 The (i+1) th element, s, representing the position of the base station 1 Representing the base station position of a reference base station, which refers toAnd the positioning label firstly acquires the position of the positioning base station, T represents the transposition of a matrix, c represents the preset signal propagation speed, and delta T (i) represents the ith element in the TDOA value.
The application relates to the technical field of tunnel positioning and discloses a ridge regression two-dimensional positioning method and system for an underground tunnel. In the method, the TDOA value is obtained by receiving the signal arrival time from different positioning base stations through the positioning tag. And further determining an observation vector and a design matrix of the least square problem according to the position of the base station. The condition number after the transpose of the design matrix and the multiplication of the design matrix are calculated to estimate the noise sensitivity, and a proper ridge regression coefficient is set based on the condition number. And finally, determining a position vector, and determining the coordinates of the positioning tag according to the position vector. Through the steps, the method overcomes the noise sensitivity commonly existing in TDOA positioning in the underground tunnel environment, and greatly improves the positioning precision and stability.
Drawings
In order to more clearly illustrate the technical solutions of the present application, the drawings that are needed in the embodiments will be briefly described below, and it will be obvious to those skilled in the art that other drawings can be obtained from these drawings without inventive effort.
FIG. 1 is a schematic workflow diagram of a two-dimensional positioning method of ridge regression for an underground tunnel according to an embodiment of the present application;
FIG. 2 is a schematic diagram of a typical positioning layout scene in a ridge regression two-dimensional positioning method for an underground tunnel according to an embodiment of the present application;
fig. 3 is a graph of relationship between ridge regression coefficients and aspect ratios of tunnel environments in a ridge regression two-dimensional positioning method for an underground tunnel according to an embodiment of the present application.
Fig. 4 is a graph showing a comparison between ridge regression positioning and least square positioning effects in a ridge regression two-dimensional positioning method for an underground tunnel according to an embodiment of the present application.
Fig. 5 is a schematic structural diagram of a two-dimensional positioning system for ridge regression for an underground tunnel according to an embodiment of the present application.
Detailed Description
In order to solve the technical problems that compared with widely used indoor positioning technology, an underground tunnel focuses on a pipe gallery environment with a large length-width ratio, the environment is constrained by geographic factors, when a traditional least square positioning method is used, as the inverse of a disease state matrix exists in a solution method, the sensitivity to noise is very high, and a very large positioning error can be caused by a small distance measurement error, the application discloses a ridge regression two-dimensional positioning method and system for the underground tunnel through the following two embodiments.
The first embodiment of the application discloses a two-dimensional positioning method of ridge regression facing an underground tunnel, the method is applied to positioning labels in the underground tunnel, a plurality of positioning base stations are arranged on two sides of a channel of the underground tunnel, and referring to a work flow schematic diagram shown in fig. 1, the two-dimensional positioning method of ridge regression facing the underground tunnel comprises:
step S101, the positioning tag acquires signals of any positioning base station, and acquires signal arrival time of any positioning base station.
Further, the positioning base station includes: UWB positioning base station, bluetooth positioning base station and ultrasonic positioning base station.
Step S102, the positioning label determines the base station position of any positioning base station according to the signals of any positioning base station.
Specifically, the local end of the positioning base station records the position of the local end, and the positioning base station continuously transmits signals carrying the position of the base station after being started.
The positioning tag receives signals from base stations at two sides of the tunnel and records the arrival time of the signals and the position of the base station.
Specifically, the positioning tag receives a signal from the positioning base station while recording the arrival time t= (t) of the signal in the order of arrival time 1 ，t 2 ，...，t M ) Where M is the total number of signals received. And decodes the position of the corresponding base station from the signal, and the position is denoted as base station position s=(s) 1 ，s 2 ，...，s M )。
Step S103, the positioning tag determines a reference signal according to the signal arrival time of any positioning base station, wherein the reference signal is the signal of the positioning base station acquired by the positioning tag first.
Step S104, the positioning tag determines a TDOA value according to the signal of any positioning base station and the reference signal, where the TDOA value is a difference between the arrival time of other signals and the arrival time of the reference signal. The other signal arrival time refers to signal arrival time of other signals except the reference signal in the signals of the positioning base station. The reference signal arrival time refers to a signal arrival time of the reference signal.
The positioning tag marks a base station from which a first arrival signal comes as a reference base station, the first arrival signal is the reference signal, all signals arriving later are subtracted from the arrival time of the signals of the reference base station to form a series of time difference values, and the time difference values are marked as TDOA values.
Specifically, the TDOA value is obtained by subtracting the arrival time t obtained in the above steps, and is expressed as Δt, and Δt= (t 2 -t 1 ，t 3 -t 1 ，...，t M -t 1 ) M-1 TDOA values in total.
Step S105, the positioning tag obtains a propagation speed of a signal, and determines an observation vector and a design matrix according to the base station position of any positioning base station, the TDOA value, and the propagation speed of the signal.
Specifically, a number of fixed-position test points are selected, and the obtained TDOA value Δt and all base station positions s are used to form a least squares problem. Wherein the observed vector in determining the least squares problem is as follows:
further, the positioning tag obtains a propagation speed of a signal, and determines an observation vector and a design matrix according to a base station position of any positioning base station, the TDOA value, and the propagation speed of the signal, including:
the observation vector is determined by the following formula:
wherein h (j) represents a j-th element of the observation vector, c represents a preset signal propagation speed, Δt (j) represents a j-th element in the TDOA value,representing the square of the vector's two norms, s j+1 The j+1th element, s, representing the base station position 1 And representing the base station position of a reference base station, wherein the reference base station refers to the position of the positioning base station acquired by the positioning tag first. The signal propagation speed c is determined in advance according to the actual application scene.
Further, the positioning tag obtains a propagation speed of a signal, and determines an observation vector and a design matrix according to a base station position of any positioning base station, the TDOA value, and the propagation speed of the signal, including:
the design matrix is determined by the following formula:
G(i，：)＝[-2(s i+1 -s 1 ) T c·Δt(i)]；
wherein G (i: represents the ith row, s of the design matrix i+1 The (i+1) th element, s, representing the position of the base station 1 And representing the base station position of a reference base station, wherein the reference base station refers to the position of the positioning base station which is firstly acquired by the positioning tag, T represents the transposition of a matrix, c represents the preset signal propagation speed, and delta T (i) represents the ith element in the TDOA value.
In the prior art, a least square formula is used to calculate a formula containing tag coordinates as follows:
θ＝(G T G) -1 G T h；
u＝θ(1∶2)；
where θ represents a position vector and u represents coordinates of the positioning tag.
But when matrix G T G is approximately singular, i.e. the condition number is extremely largeSince the sensitivity of the least square method to noise is stronger, a great error may be generated, and thus the phenomenon is alleviated by using a ridge regression positioning method, and the specific method is as follows.
And S106, determining a ridge regression coefficient by the positioning label according to the design matrix and the preset condition number limit.
In some embodiments of the present application, the condition number is limited to a condition number less than 1000.
Further, the positioning tag determines a ridge regression coefficient according to the design matrix and a preset condition number limit, including:
the ridge regression coefficients are determined by the following formula:
min λ＞0 λ；
s.t.cond(G T G+λI)＜1000；
wherein λ represents the ridge regression coefficient, cond (·) represents the condition number of the matrix, G represents the design matrix, T represents the transpose of the matrix, I represents the identity matrix, the number of rows and columns of the identity matrix I and G T The number of rows and columns of G is the same.
Specifically, the size of λ is defined by matrix G T The condition number of g+λi is determined, the condition number being defined as the ratio of the maximum eigenvalue to the minimum eigenvalue of the matrix, the condition number deviating from 1 indicating that the singularity of the matrix is more serious. The introduction of the ridge regression coefficient lambda reduces the matrix G T The condition number of G reduces the sensitivity of the least square method to noise, and meanwhile, the oversized person can bring positioning deviation, so that a reasonable ridge regression coefficient lambda is set by adopting the formula. Make G T The minimum ridge regression coefficient lambda with a condition number G + lambda I of less than 1000 ensures a low sensitivity and high accuracy of the positioning.
In step S107, the location tag determines a location vector according to the observation vector, the design matrix, and the ridge regression coefficient.
Further, the positioning tag determines a position vector according to the observation vector, the design matrix, and the ridge regression coefficient, including:
the position vector is determined by the following formula:
θ＝(G T G+λI) -1 G T h；
wherein θ represents the position vector, G represents the design matrix, T represents the transpose of the matrix, λ represents the ridge regression coefficient, h represents the observation vector, I represents the identity matrix, and the number of rows and columns of the identity matrix I and G T G has the same rank number, namely the size of the identity matrix I is equal to that of G T G is the same.
Step S108, the positioning label determines the coordinates of the positioning label according to the position vector.
Further, the positioning tag determines coordinates of the positioning tag according to the position vector, including:
the coordinates of the positioning tag are determined by the following formula:
u＝θ(1∶2)；
where u represents the coordinates of the positioning tag and θ (1:2) represents the first two elements of the position vector θ.
Referring to fig. 2, a typical scenario for implementing the embodiments of the present application is a tunnel environment, where base stations are typically disposed on both sides of the tunnel, and where a located tag may be located at any point within the tunnel environment, without loss of generality, the embodiment selects a quarter point in the major axis direction and a center point in the minor axis direction as the location of the tag, where there is typical error sensitivity, and may be used to select a suitable ridge regression coefficient for locating the tag location under the layout.
Referring to fig. 3, in a typical scenario, the present embodiment verifies the ridge regression coefficients determined in step S106 in tunnel environments with different aspect ratios, as a graph of ridge regression coefficients versus tunnel environment aspect ratios. The ridge regression coefficients for the four aspect ratio conditions were examined in fig. 3 and show that the ridge regression coefficients are positively correlated with the aspect ratio.
Referring to fig. 4, a graph comparing the effect of ridge regression positioning with that of least square positioning in the prior art in the embodiment of the present application shows that the ridge regression positioning has significantly reduced errors compared with the least square positioning under four aspect ratios, and has relatively stable positioning performance under different aspect ratios, and no significant relation with the aspect ratio.
According to the ridge regression two-dimensional positioning method for the underground tunnel, which is disclosed by the embodiment of the application, firstly, the arrival time of signals from different positioning base stations is received through the positioning label, and the TDOA value is obtained. And further determining an observation vector and a design matrix of the least square problem according to the position of the base station. The condition number after the transpose of the design matrix and the multiplication of the design matrix are calculated to estimate the noise sensitivity, and a proper ridge regression coefficient is set based on the condition number. And finally, determining a position vector, and determining the coordinates of the positioning tag according to the position vector. Through the steps, the method overcomes the noise sensitivity commonly existing in TDOA positioning in the underground tunnel environment, and greatly improves the positioning precision and stability.
The following are system embodiments of the present application, which may be used to perform method embodiments of the present application. For details not disclosed in the system embodiments of the present application, please refer to the method embodiments of the present application.
The second embodiment of the application discloses a two-dimensional positioning system of ridge regression facing to an underground tunnel, the two-dimensional positioning system of ridge regression facing to an underground tunnel applies the two-dimensional positioning method of ridge regression facing to an underground tunnel disclosed in the first embodiment of the application, the system is applied to positioning labels in an underground tunnel, two sides of a channel of the underground tunnel are provided with a plurality of positioning base stations, see a structure schematic diagram shown in fig. 5, and the two-dimensional positioning system of ridge regression facing to the underground tunnel comprises:
the signal receiving module 10 is configured to obtain a signal of any positioning base station from the positioning tag, and obtain a signal arrival time of the any positioning base station.
The base station position obtaining module 20 is configured to determine a base station position of the any positioning base station according to the signal of the any positioning base station.
The reference signal obtaining module 30 is configured to determine a reference signal according to the signal arrival time of the positioning base station, where the reference signal is a signal of the positioning base station that is first obtained by the positioning tag.
The TDOA value determining module 40 is configured to determine a TDOA value according to the signal of the any positioning base station and the reference signal, where the TDOA value is a difference between the arrival time of the other signal and the arrival time of the reference signal. The other signal arrival time refers to signal arrival time of other signals except the reference signal in the signals of the positioning base station. The reference signal arrival time refers to a signal arrival time of the reference signal.
The vector and matrix processing module 50 is configured to obtain a propagation speed of a signal from the positioning tag, and determine an observation vector and a design matrix according to a base station position of the any positioning base station, the TDOA value, and the propagation speed of the signal.
Further, the vector and matrix processing module 50 is configured to determine the observation vector by the following formula:
wherein h (j) represents a j-th element of the observation vector, c represents a preset signal propagation speed, Δt (j) represents a j-th element in the TDOA value,representing the square of the vector's two norms, s j+1 The j+1th element, s, representing the base station position 1 And representing the base station position of a reference base station, wherein the reference base station refers to the position of the positioning base station acquired by the positioning tag first.
Further, the vector and matrix processing module 50 is configured to determine the design matrix by the following formula:
G(i，：)＝[-2(s i+1 -s 1 ) T c·Δt(i)]；
wherein G (i: represents the ith row, s of the design matrix i+l The (i+1) th element, s, representing the position of the base station 1 Representing the base station position of a reference base station, which refers to the positioning tagThe position of the positioning base station acquired first, T represents the transpose of the matrix, c represents the preset signal propagation speed, and Δt (i) represents the ith element in the TDOA value.
The ridge regression coefficient determining module 60 is configured to determine a ridge regression coefficient according to the design matrix and a preset condition number limit.
Further, the ridge regression coefficient determination module 60 is configured to determine the ridge regression coefficient by the following formula:
min λ＞0 λ；
s.t.cond(G T G+λI)＜1000；
wherein λ represents the ridge regression coefficient, cond (·) represents the condition number of the matrix, G represents the design matrix, T represents the transpose of the matrix, I represents the identity matrix, the number of rows and columns of the identity matrix I and G T The number of rows and columns of G is the same.
A position vector determination module 70 for the location tag to determine a position vector based on the observation vector, the design matrix, and the ridge regression coefficients.
Further, the location vector determining module 70 is configured to determine the location vector by the following formula:
θ＝(G T G+λI) -1 G T h；
wherein θ represents the position vector, G represents the design matrix, T represents the transpose of the matrix, λ represents the ridge regression coefficient, h represents the observation vector, I represents the identity matrix, and the number of rows and columns of the identity matrix I and G T The number of rows and columns of G is the same.
And the positioning module 80 is used for determining the coordinates of the positioning label according to the position vector by the positioning label.
Further, the positioning module 80 is configured to determine the coordinates of the positioning tag by the following formula:
u＝θ(1∶2)；
where u represents the coordinates of the positioning tag and θ (1:2) represents the first two elements of the position vector θ.
It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the scope of protection thereof, and although the present invention has been described in detail with reference to the above embodiments, it should be understood by those of ordinary skill in the art that: various changes, modifications, or equivalents may be made to the particular embodiments of the invention by those skilled in the art after reading the present disclosure, but such changes, modifications, or equivalents are within the scope of the invention as defined in the appended claims.

Claims (5)

1. The ridge regression two-dimensional positioning method for the underground tunnel is characterized by being applied to positioning labels in the underground tunnel, wherein a plurality of positioning base stations are arranged on two sides of a channel of the underground tunnel, and the ridge regression two-dimensional positioning method for the underground tunnel comprises the following steps:
the positioning tag acquires signals of any positioning base station and acquires signal arrival time of the any positioning base station;
the positioning tag determines the base station position of any positioning base station according to the signals of any positioning base station;
the positioning tag determines a reference signal according to the signal arrival time of any positioning base station, wherein the reference signal is a signal of the positioning base station which is firstly acquired by the positioning tag;
the positioning tag determines a TDOA value according to the signal of any positioning base station and the reference signal, wherein the TDOA value refers to the difference value between the arrival time of other signals and the arrival time of the reference signal; the other signal arrival time refers to signal arrival time of other signals except the reference signal in the signals of the positioning base station; the reference signal arrival time refers to a signal arrival time of the reference signal;
the positioning tag obtains the propagation speed of signals and determines an observation vector and a design matrix according to the base station position of any positioning base station, the TDOA value and the propagation speed of the signals;
the positioning label determines a ridge regression coefficient according to the design matrix and a preset condition number limit;
the positioning label determines a position vector according to the observation vector, the design matrix and the ridge regression coefficient;
the positioning label determines the coordinates of the positioning label according to the position vector;
the condition number is limited to a condition number less than 1000;
the positioning tag determines a ridge regression coefficient according to the design matrix and a preset condition number limit, and comprises:
the ridge regression coefficients are determined by the following formula:
；
；
wherein,representing the ridge regression coefficient, < >>Condition number, ∈ representing matrix>Representing the design matrix->Representing the transpose of the matrix>Representing an identity matrix, identity matrix->Row and column number of (2)>The number of rows and columns is the same;
the positioning tag determines a position vector according to the observation vector, the design matrix and the ridge regression coefficient, and comprises:
the position vector is determined by the following formula:
；
wherein,representing the position vector,/->Representing the design matrix->Representing the transpose of the matrix>Representing the ridge regression coefficient, < >>Representing the observation vector,/->Representing an identity matrix, identity matrix->Row and column number of (2)>The number of rows and columns is the same;
the positioning tag obtains the propagation speed of a signal, and determines an observation vector and a design matrix according to the base station position of any positioning base station, the TDOA value and the propagation speed of the signal, including:
the observation vector is determined by the following formula:
；
wherein,represents the +.>Element(s)>Representing a preset signal propagation speed, +.>Represents the +.about.in the TDOA value>Element(s)>Representing the square of the vector's two norms, +.>A +.o. representing the location of the base station>Element(s)>Representing the base station position of a reference base station, wherein the reference base station refers to the position of a positioning base station which is acquired by the positioning tag first;
the positioning tag obtains the propagation speed of a signal, and determines an observation vector and a design matrix according to the base station position of any positioning base station, the TDOA value and the propagation speed of the signal, including:
the design matrix is determined by the following formula:
；
wherein,representing the +.>Go (go)/(go)>A +.o. representing the location of the base station>Element(s)>Representing the base station position of a reference base station, which refers to the position of the positioning base station that the positioning tag first acquired,/for>Representing the transpose of the matrix>Representing a preset signal propagation speed, +.>Represents the +.about.in the TDOA value>The elements.
2. The method of claim 1, wherein the determining the coordinates of the positioning tag based on the position vector comprises:
the coordinates of the positioning tag are determined by the following formula:
；
wherein,representing the coordinates of the positioning tag, +.>Representing the position vector +.>Is a first two elements of (c).
3. The underground tunnel-oriented ridge regression two-dimensional positioning method of claim 1, wherein the positioning base station comprises: UWB positioning base station, bluetooth positioning base station and ultrasonic positioning base station.
4. An underground tunnel-oriented ridge regression two-dimensional positioning system, which is characterized in that the underground tunnel-oriented ridge regression two-dimensional positioning system is applied to the underground tunnel-oriented ridge regression two-dimensional positioning method according to any one of claims 1-3, the system is applied to positioning labels in an underground tunnel, a plurality of positioning base stations are arranged on two sides of a passage of the underground tunnel, and the underground tunnel-oriented ridge regression two-dimensional positioning system comprises:
the signal receiving module is used for acquiring signals of any positioning base station by the positioning tag and acquiring signal arrival time of any positioning base station;
the base station position acquisition module is used for determining the base station position of any positioning base station according to the signals of any positioning base station by the positioning tag;
the reference signal acquisition module is used for determining a reference signal according to the signal arrival time of any positioning base station by the positioning tag, wherein the reference signal is a signal of the positioning base station which is acquired by the positioning tag first;
the TDOA value determining module is used for determining a TDOA value according to the signal of any positioning base station and the reference signal, wherein the TDOA value refers to the difference value between the arrival time of other signals and the arrival time of the reference signal; the other signal arrival time refers to signal arrival time of other signals except the reference signal in the signals of the positioning base station; the reference signal arrival time refers to a signal arrival time of the reference signal;
the vector and matrix processing module is used for acquiring the propagation speed of the signals by the positioning tag and determining an observation vector and a design matrix according to the base station position of any positioning base station, the TDOA value and the propagation speed of the signals;
the ridge regression coefficient determining module is used for determining a ridge regression coefficient according to the design matrix and the preset condition number limit by the positioning label;
the position vector determining module is used for determining a position vector according to the observation vector, the design matrix and the ridge regression coefficient by the positioning label;
and the positioning module is used for determining the coordinates of the positioning label according to the position vector by the positioning label.
5. The underground tunnel-oriented ridge regression two-dimensional positioning system of claim 4, wherein the ridge regression coefficient determination module is configured to determine the ridge regression coefficient by the following equation:
；
；
wherein,representing the LinghuiRadix Angelicae sinensis coefficient (herba Polygoni Avicularis)>Condition number, ∈ representing matrix>Representing the design matrix->Representing the transpose of the matrix>Representing an identity matrix, identity matrix->Row and column number of (2)>The number of rows and columns is the same.
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